Many people (including dictionaries) seem to think that federalism refers to a strong centralized government. They will actually look at me as if I had just told them that 9/11 was an inside job when I explain that federalism refers to decentralized government.
I think the confusion comes from the terminology used. Gary Galles explains:
Federalism refers to the system of decentralized government. This group [Antifederalists] defended states rights — the very essence of federalism — against the Federalists, who would have been more accurately described as Nationalists.
Hitler understood federalism, which is why he was against it:
Hitler praises Otto von Bismarck for proving “the greatness of his statesmanship” by gradually diminishing the sovereignty of the German states and centralizing governmental power in Germany. This was a most welcome development, Hitler wrote, since the power of the central state in Germany was supposedly threatened by “the struggle between federalism and centralization so shrewdly propagated by the Jews in 1919-20-21 and afterward . . .” (p. 565). Federalism is “a league of sovereign states which ban together of their own free will, on the strength of their sovereignty” to cede some (but not all) of their sovereignty to form “the common federation” (p. 566). Hitler was violently opposed to such a system.
Anti-federalists support federalism – states rights; decentralized power; Jefferson; libertarian
Federalists support Totalitarianism – centralized power; Lincoln; Hitler; statist; fascist; nationalist
More on the advantages of federalism here.